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Factorials (!) and Divisibility

It’s amazing how something as simple as a (!) symbol can throw us all for a loop, even when really we’re just looking at a very simple divisibility question. This is my own question designed to mimic a GMATPrep question.

Start by setting a timer for 2-minutes and try this one on your own, then scroll down for the explanation!

Which of the following is an integer?

I. 10! / 3! II. 9! / 8! III. 13! / 11! 5!

A) I only B) II only C) III only D) I and II only E) I, II, and III

Explanation:

If the result of a fraction is an integer that means that what is in the denominator divides evenly into what is in the numerator. The question for each of these Roman numerals becomes: will the denominator go evenly into the numerator?